Đáp án:
`(x^2+2x+3)/2`
Giải thích các bước giải:
Với `x\ne+-1`
`(x+2)/(x-1).(x^3/(2x+2)+1)-(8x+7)/(2x^2-2)`
`=(x+2)/(x-1).(x^3+2x+2)/(2x+2)-(8x+7)/(2x^2-2)`
`=((x+2).(x^3+2x+2))/((x-1)(2x+2))-(8x+7)/(2x^2-2)`
`=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2x^2-2)`
`=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2(x^2-1))`
`=((x+2).(x^3+2x+2))/(2(x-1)(x+1))-(8x+7)/(2(x-1)(x+1))`
`=((x+2).(x^3+2x+2)-(8x+7))/(2(x-1)(x+1))`
`=(x^4+2x^2+2x+2x^3+4x+4-(8x+7))/(2(x-1)(x+1))`
`=(x^4+2x^3+2x^2+6x+4-8x-7)/(2(x-1)(x+1))`
`=(x^4+2x^3+2x^2-2x-3)/(2(x-1)(x+1))`
`=(x^4-x^2+2x^3-2x+3x^2-3)/(2(x-1)(x+1))`
`=(x^2(x^2-1)+2x(x^2-1)+3(x^2-1))/(2(x^2-1))`
`=((x^2-1)(x^2+2x+3))/(2(x^2-1))`
`=(x^2+2x+3)/2`
